Reflection of Light and Mirrors
In December 1993, NASA astronauts aboard Space Shuttle Endeavour installed COSTAR (Corrective Optics Space Telescope Axial Replacement) on the Hubble Space Telescope — the primary mirror had been ground 2.2 micrometres too flat, blurring every image. COSTAR inserted corrective optics that exactly compensated for the mirror error: resolution improved from 0.1 arcsecond to 0.05 arcsecond (a factor of 2), transforming Hubble from a scientific embarrassment into the most productive telescope in history. Every correction relied on the same law of reflection you will learn in this lesson.
A plane (flat) mirror produces your reflection. The image appears to be behind the mirror. Is it a real image (formed by actual rays) or a virtual image (formed by apparent extension of reflected rays)? Predict and explain.
Warm-up — the law of reflection states:
Know
- Law of reflection: $\theta_i = \theta_r$ (from the normal)
- Plane mirror: virtual, upright, same-size image as far behind as object is in front
- Concave mirror: can produce real (inverted) or virtual (upright, magnified) images
Understand
- The difference between real and virtual images
- How a concave mirror focuses parallel rays at its focal point
- How to draw ray diagrams using the three principal rays
Can Do
- Draw and interpret reflection ray diagrams
- Describe images formed by plane and concave mirrors
- Apply mirror properties to real-world examples
Core Content
Stand 1 metre in front of a bathroom mirror and your reflection stares back at you — same height, same size, upright, apparently sitting 1 metre behind the glass. Reach out to touch the image: your hand hits the mirror surface, not the image — because the image is not actually there. Move closer: the reflection moves closer too, always at the same distance behind the mirror as you are in front. That is the observable behaviour of a plane mirror, and it follows entirely from $\theta_i = \theta_r$.
In a plane mirror, each reflected ray appears to come from a point behind the mirror. The image is virtual (behind the mirror), upright, laterally reversed (left-right), and the same size as the object. The image distance equals the object distance.
Plane mirror image: virtual, upright, same size, laterally reversed; image distance = object distance. The image cannot be projected because reflected rays only appear to meet behind the mirror — they do not actually converge.
Pause — write the highlighted plane mirror image rules into your book before moving on.
We just saw that a plane mirror always produces a virtual, upright, same-size image. That raises a question: can a mirror ever produce a real image that can be projected onto a screen? This card answers it → yes — a concave mirror converges reflected rays to a real focal point, and whether the image is real or virtual depends on where the object sits relative to that focal point.
A concave mirror curves inward. Parallel rays reflect through the focal point $F$. Image type depends on object distance:
| Object distance | Image type | Properties |
|---|---|---|
| Beyond $C$ (2F) | Real | Inverted, smaller, between $F$ and $C$ |
| At $C$ (2F) | Real | Inverted, same size, at $C$ |
| Between $F$ and $C$ | Real | Inverted, enlarged, beyond $C$ |
| Closer than $F$ | Virtual | Upright, magnified, behind mirror |
Concave (converging) mirror: object beyond $F$ → real, inverted image (projectable); object inside $F$ → virtual, upright, magnified image. Convex (diverging) mirror: always virtual, upright, smaller. Focal length $f = R/2$ where $R$ is radius of curvature.
Add the highlighted concave mirror image rules and the focal length formula to your notes before the check below.
An object is placed closer than the focal length in front of a concave mirror. The image is:
A virtual image can be projected onto a screen.
In a plane mirror, the image is the same distance behind the mirror as the object is in front.
Activities
Draw ray diagrams for: (a) an object 30 cm in front of a plane mirror, (b) an object 40 cm from a concave mirror with $f = 20$ cm, (c) an object 10 cm from a concave mirror with $f = 20$ cm. For each, describe the image (real/virtual, upright/inverted, size).
A reflecting telescope uses a large concave mirror rather than a lens. Explain two advantages of using a mirror for a large astronomical telescope.
For each description of an image, identify which type of mirror produced it:
- Always virtual, upright, smaller — used as a car's side mirror
- Virtual, upright, magnified — used as a make-up mirror
- Real, inverted — can be projected onto a screen
Which is NOT a property of the image in a plane mirror?
An object is placed at the centre of curvature $C$ of a concave mirror (i.e. at distance $2f$). The image is:
Which type of mirror is used in car rear-view mirrors to provide a wide field of view?
UnderstandBand 3(3 marks) 1. Distinguish between a real and a virtual image. Give one example of each from mirror optics.
ApplyBand 4(3 marks) 2. Draw (or describe in detail) a ray diagram for an object placed between the focal point and the mirror surface of a concave mirror. Describe the image fully (type, orientation, size, location).
AnalyseBand 5(4 marks) 3. Explain why the Anglo-Australian Telescope uses a large concave parabolic mirror rather than a lens. In your answer discuss: chromatic aberration, support of the optic, light-gathering power.
Show all answers
Short Answer — Model Answers
Q1 (3 marks): A real image is formed where reflected (or refracted) rays actually converge; it can be projected on a screen and is inverted. Example: object beyond focal point of concave mirror. A virtual image is formed where rays appear to come from but do not actually converge; it cannot be projected and is upright. Example: image in a plane mirror (behind the mirror).
Q2 (3 marks): A parallel ray reflects through $F$; a ray aimed toward $F$ reflects parallel. Both reflected rays diverge — traced back behind the mirror they appear to come from a point behind the mirror. Image: virtual, upright, magnified, located behind the mirror.
Q3 (4 marks): (1) Chromatic aberration: lenses refract different wavelengths by different amounts (dispersion), blurring coloured stars. Mirrors reflect all wavelengths at identical angles — no chromatic aberration. (2) Support: glass/silica lenses can only be supported at their edges; at 3.9 m diameter they sag under gravity. Mirrors can be supported across their entire back surface. (3) Light-gathering: the 3.9 m diameter collects area $\pi r^2 \approx 12$ m² compared to a human pupil of ~0.007 m² — about 1700× more light per unit time.
Hubble's 1993 story makes the stakes of mirror geometry concrete: the primary mirror was ground 2.2 micrometres too flat, so incoming starlight was not converging to the correct focal point — real images were blurred. COSTAR inserted corrective mirrors that exactly re-converged the rays, restoring resolution from 0.1 to 0.05 arcseconds. Every adjustment required precise knowledge of where real images form relative to the focal point — the same geometry you worked through in this lesson. The image in a plane mirror is virtual (no rays actually meet behind it); in a concave mirror, real images form on the same side as the object when it is beyond the focal point.